I was wondering what relation and differences are between causal inference and prediction (classification and regression)?

For example,

In prediction, we have predictor/input variables and response/output variables. Does that mean that there is causal relation between input and output variables? So does prediction belong to causal inference?

If I understand correctly, causal inference considers to estimate conditional distribution of one random variable given another random variable, and often use graphical models to represent the conditional independence between random variables. So causal inference in this sense isn't prediction, is it?

Thanks and regards!